Advertisements
Advertisements
Question
Find the two natural numbers which differ by 5 and the sum of whose squares is 97.
Solution
Let the two numbers be x and x + 5.
From the given information,
x2 + (x + 5)2 = 97
2x2 + 10x + 25 – 97 = 0
2x2 + 10x – 72 = 0
x2 + 5x – 36 = 0
(x + 9)(x – 4) = 0
x = –9 or 4
Since, –9 is not a natural number.
So, x = 4.
Thus, the numbers are 4 and 9.
APPEARS IN
RELATED QUESTIONS
The sum of a number and its reciprocal is 4.25. Find the number.
Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is `7/10`.
The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.
Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.
The product of the digits of a two digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.
Given that the sum of the squares of the first seven natural numbers is 140, then their mean is ______.
The sum of a number and its reciprocal is 5.2. The number is ______.
The product of two whole numbers, each greater than 4, is 35; the numbers are ______.
If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is ______.
The sum of two whole numbers is 18 and their product is 45, the numbers are ______.
